Note that the optimal cooperative IRS passive beamforming for maximizing \(r^{\rm (M)}_{\mathrm {S,R}}\)  in (REF ) is difficult to obtain due to the non-convex unit-modulus constraint as well as the coupling between \(\Phi _{\mathrm {I}_1,{\mathrm {S,R}}}\)  and \(\Phi _{\mathrm {I}_2,{\mathrm {S,R}}}\)  in the effective channel gain (see (REF )). Although a suboptimal solution can be obtained by designing an iterative algorithm using e.g., the semidefinite relaxation (SDR) and block coordinate descent (BCD) techniques [1]}, [2]}, it yields little insight into the achievable rate under this IRS deployment strategy. To address this issue, we focus on characterizing the capacity scaling order for the multi-IRS deployment in the sequel.
We first derive the lower and upper bounds on the capacity given in (REF ), and then obtain its scaling order when \(M\rightarrow \infty \) .
